Symmetry group classification of variable coefficient mKdV equation

Symmetry group classifications of variable coefficient mKdV equation is performed by using the classical infinitesimal Lie method, the technique of equivalence transformations and the theory of classification of abstract low-dimensional Lie algebras. It is shown that there are four and six inequivalent mKdV-type nonlinear evolution equations admitting one- and two-dimensional solvable Lie algebras, respectively. Furthermore, we prove that there exist no equation admitting three- and higer-dimensional Lie algebras.